This invention relates to a method and apparatus for circular interpolation and, more particularly, to a method and apparatus for circular interpolation in a numerical control system wherein circular interpolation is performed by giving the center of an arc as well as the starting and end points of the arc.
A numerical control system generally is equipped with a circular interpolation function. Such a system is disclosed in the FANUC 200C Operator's Manual, pp. 61-64 (published by Fujitsu Fanuc, December, 1979). In order to move a tool or table along an arc, the numerical control system executes a circular interpolation operation on the basis of information such as the center, starting and end points of the arc, and distributed pulses X.sub.p, Y.sub.p indicative of movement along the X-axis and Y-axis are generated as a result of the interpolation operation. The distributed pulses X.sub.p, Y.sub.p are applied to servo circuits which respond by driving X- and Y-axis motors to transport the tool along the instructed arc so that the tool may machine the desired arc into a workpiece.
In the conventional numerical control system that employs the aforementioned circular interpolation method, a disadvantage arises when the distances r.sub.A, r.sub.B from the center to the starting and end points of the arc, respectively, are different, the center, starting and end points of the arc being specified by the program. When such is the case, as shown in FIG. 1, the tool is so controlled as to move from the starting point P.sub.s to the point P.sub.e ' along the arc CA' of radius r.sub.A and center 0, and then from the point P.sub.e ' to the end point P.sub.e. This lowers cutting precision and is undesirable in cases where high precision is required, as in machining with a wire-type electric discharge machine. Further, with such a machine so-called "back-up" control may be applied to move the wire electrode backwardly along the previously cut path when the wire comes into contact with the workpiece, but back-up control is difficult to carry out when the wire moves in the manner described above. It should be noted that a situation in which r.sub.A and r.sub.B are unequal may arise as the result of a calculation error or the like during programming.
Thus there is a need for a numerical control system that is capable of moving a tool along a curve which smoothly connects the starting point P.sub.s and end point P.sub.e of an arc even when r.sub.A and r.sub.B in the given arc interpolation instruction are unequal.